Subgroups — C₂×#23777803 #35196068

Order 20224.

8802 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777803	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099306	C₂	1	2	yes	maximal, complemented
3	C₂×#19099305	C₂	1	2	yes	maximal, complemented
4	C₂×#19099277	C₂	1	2	yes	maximal, complemented
5	C₂×#19099276	C₂	1	2	yes	maximal, complemented
6	C₂×#19099275	C₂	1	2	yes	maximal, complemented
7	C₂×#19099197	C₂	1	2	yes	maximal, complemented
8	C₂×D₄×C₂²⋊D₇₉	C₂	1	2	yes	maximal, complemented
9	C₂×#19099195	C₂	1	2	yes	maximal, complemented
10	C₂×#19099129	C₂	1	2	yes	maximal, complemented
11	C₂×#19099128	C₂	1	4	yes	maximal, complemented
12	C₂×#19099127	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#19099126	C₂	1	4	yes	maximal, complemented
14	C₂×#19099109	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#19099108	C₂	1	2	yes	maximal, complemented
16	C₂×#535×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#11929624	C₂²	1	1	yes	characteristic, complemented
18	C₂²×#11929623	C₂²	1	4	yes	complemented
19	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
21	C₂²×D₄×D₇₉	C₂²	1	4	yes	complemented
22	C₂²×D₄×D₇₉	C₂²	1	2	yes	complemented
23	#19099306	C₂²	1	32	yes	complemented
24	#19099305	C₂²	1	32	yes	complemented
25	#19099277	C₂²	1	32	yes	complemented
26	#19099276	C₂²	1	32	yes	complemented
27	#19099275	C₂²	1	32	yes	complemented
28	#19099197	C₂²	1	32	yes	complemented
29	D₄×C₂²⋊D₇₉	C₂²	1	32	yes	complemented
30	#19099195	C₂²	1	32	yes	complemented
31	#19099129	C₂²	1	32	yes	complemented
32	#19099128	C₂²	1	64	yes	complemented
33	#19099127	C₂²	1	16	yes	complemented
34	#19099126	C₂²	1	64	yes	complemented
35	#19099109	C₂²	1	16	yes	complemented
36	#19099108	C₂²	1	32	yes	complemented
37	C₂×#14579160	C₂²	1	2	yes	complemented
38	C₂×#14579159	C₂²	1	1	yes	characteristic, complemented
39	C₂×#14579157	C₂²	1	1	yes	characteristic
40	C₂×#14579157	C₂²	1	2	yes	—
41	C₂×#14579157	C₂²	1	4	yes	complemented
42	C₂×#14579157	C₂²	1	2	yes	complemented
43	C₂×#14579150	C₂²	1	1	yes	characteristic, complemented
44	C₂×#14579150	C₂²	1	2	yes	complemented
45	C₂×#14579149	C₂²	1	4	yes	complemented
46	C₂×#14579148	C₂²	1	1	yes	characteristic, complemented
47	C₂×#14579148	C₂²	1	4	yes	complemented
48	C₂×#14579147	C₂²	1	4	yes	complemented
49	C₂×#14579147	C₂²	1	4	yes	complemented
50	C₂×#14579147	C₂²	1	4	yes	complemented
51	C₂×#14579147	C₂²	1	4	yes	complemented
52	C₂×#14579136	C₂²	1	2	yes	complemented
53	C₂×#14579135	C₂²	1	2	yes	complemented
54	C₂×#14579135	C₂²	1	2	yes	complemented
55	C₂×#14579134	C₂²	1	4	yes	complemented
56	C₂×#14579134	C₂²	1	4	yes	complemented
57	C₂×#14579133	C₂²	1	4	yes	complemented
58	C₂×#14579133	C₂²	1	4	yes	complemented
59	C₂×#14579133	C₂²	1	4	yes	complemented
60	C₂×#14579133	C₂²	1	2	yes	complemented
61	C₂×#14579133	C₂²	1	2	yes	complemented
62	C₂×#14579132	C₂²	1	2	yes	complemented
63	C₂×#14579131	C₂²	1	4	yes	complemented
64	C₂×#14579131	C₂²	1	4	yes	complemented
65	C₂×#14579130	C₂²	1	4	yes	complemented
66	C₂×#14579129	C₂²	1	2	yes	complemented
67	C₂×#14579129	C₂²	1	4	yes	complemented
68	C₂×#14579129	C₂²	1	4	yes	complemented
69	C₂×#14579129	C₂²	1	2	yes	complemented
70	C₂×#14579129	C₂²	1	4	yes	complemented
71	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
72	C₂×#14579123	C₂²	1	2	yes	complemented
73	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
74	C₂×C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
75	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	4	yes	complemented
76	C₂×#14579120	C₂²	1	1	yes	characteristic, complemented
77	C₂×#14579119	C₂²	1	2	yes	complemented
78	C₂×#14579118	C₂²	1	4	yes	complemented
79	C₂×#14579117	C₂²	1	4	yes	complemented
80	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
81	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic, complemented
82	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
83	#535×C₇₉	C₂²	1	16	yes	complemented
84	C₂×#127×C₇₉	C₂²	1	2	yes	complemented
85	C₂×#124×C₇₉	C₂²	1	2	yes	complemented
86	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
87	C₂×#121×C₇₉	C₂²	1	2	yes	complemented
88	C₂×#120×C₇₉	C₂²	1	2	yes	complemented
89	C₂×#120×C₇₉	C₂²	1	2	yes	complemented
90	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic, complemented
91	C₂⁴×D₇₉	C₂³	1	2	yes	—
92	C₂⁴×D₇₉	C₂³	1	4	yes	—
93	C₂×#11929624	—	4	4	no	—
94	C₂×#11929624	C₂³	1	8	yes	complemented
95	C₂×#11929623	—	4	16	no	—
96	C₂×#11929623	C₂³	1	32	yes	complemented
97	C₂²×Dic₁₅₈	C₂³	1	1	yes	characteristic
98	C₂²×Dic₁₅₈	C₂³	1	4	yes	—
99	C₂²×D₃₁₆	—	4	4	no	—
100	C₂²×D₃₁₆	C₂³	1	2	yes	—
101	C₂²×D₃₁₆	C₂³	1	1	yes	characteristic
102	C₂²×D₃₁₆	C₂³	1	2	yes	—
103	C₂²×D₃₁₆	C₂³	1	4	yes	—
104	C₂²×D₃₁₆	C₂³	1	8	yes	complemented
105	C₂²×C₂²⋊D₇₉	—	4	16	no	—
106	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
107	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
108	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
109	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
110	C₂²×C₂²⋊D₇₉	C₂³	1	2	yes	—
111	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
112	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
113	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
114	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
115	C₂²×C₂²⋊D₇₉	C₂³	1	32	yes	complemented
116	C₂×D₄×D₇₉	—	4	16	no	—
117	C₂×D₄×D₇₉	—	4	8	no	—
118	C₂×D₄×D₇₉	C₂³	1	32	yes	complemented
119	C₂×D₄×D₇₉	C₂³	1	16	yes	complemented
120	C₂³×Dic₇₉	C₂³	1	2	yes	—
121	C₂³×Dic₇₉	C₂³	1	4	yes	—
122	C₂²×C₄×D₇₉	C₂³	1	4	yes	—
123	C₂²×C₄×D₇₉	C₂³	1	2	yes	—
124	#14579160	C₂³	1	16	yes	complemented
125	#14579159	C₂³	1	8	yes	complemented
126	#14579157	C₂³	1	8	yes	—
127	#14579157	C₂³	1	16	yes	—
128	#14579157	C₂³	1	32	yes	complemented
129	#14579157	C₂³	1	16	yes	complemented
130	#14579150	C₂³	1	16	yes	complemented
131	#14579150	C₂³	1	8	yes	complemented
132	#14579149	C₂³	1	32	yes	complemented
133	#14579148	C₂³	1	32	yes	complemented
134	#14579148	C₂³	1	8	yes	complemented
135	#14579147	C₂³	1	32	yes	complemented
136	#14579147	C₂³	1	32	yes	complemented
137	#14579147	C₂³	1	32	yes	complemented
138	#14579147	C₂³	1	32	yes	complemented
139	#14579136	C₂³	1	16	yes	complemented
140	#14579135	C₂³	1	16	yes	complemented
141	#14579135	C₂³	1	16	yes	complemented
142	#14579134	C₂³	1	32	yes	complemented
143	#14579134	C₂³	1	32	yes	complemented
144	#14579133	C₂³	1	32	yes	complemented
145	#14579133	C₂³	1	32	yes	complemented
146	#14579133	C₂³	1	32	yes	complemented
147	#14579133	C₂³	1	16	yes	complemented
148	#14579133	C₂³	1	16	yes	complemented
149	#14579132	C₂³	1	16	yes	complemented
150	#14579131	C₂³	1	32	yes	complemented
151	#14579131	C₂³	1	32	yes	complemented
152	#14579130	C₂³	1	32	yes	complemented
153	#14579129	C₂³	1	16	yes	complemented
154	#14579129	C₂³	1	32	yes	complemented
155	#14579129	C₂³	1	32	yes	complemented
156	#14579129	C₂³	1	16	yes	complemented
157	#14579129	C₂³	1	32	yes	complemented
158	D₄×Dic₇₉	C₂³	1	16	yes	complemented
159	#14579123	C₂³	1	16	yes	complemented
160	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
161	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
162	(C₂²⋊D₇₉)⋊C₄	C₂³	1	32	yes	complemented
163	#14579120	C₂³	1	8	yes	complemented
164	#14579119	C₂³	1	16	yes	complemented
165	#14579118	C₂³	1	32	yes	complemented
166	#14579117	C₂³	1	32	yes	complemented
167	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
168	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
169	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
170	C₂×Dic₇₉⋊C₄	C₂³	1	2	yes	—
171	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
172	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
175	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
176	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
177	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
178	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
179	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
180	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
181	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
182	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
183	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
184	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
185	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
186	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
187	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
188	C₂×C₄×Dic₇₉	C₂³	1	8	yes	complemented
189	C₂⁵×C₇₉	C₂³	1	2	yes	—
190	C₂×#41×C₇₉	—	4	4	no	—
191	C₂×#41×C₇₉	C₂³	1	8	yes	complemented
192	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
193	C₂²×D₄×C₇₉	—	4	4	no	—
194	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
195	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
196	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
197	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
198	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
199	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
200	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
201	C₂²×D₄×C₇₉	C₂³	1	8	yes	complemented
202	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
203	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
204	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
205	#127×C₇₉	C₂³	1	16	yes	complemented
206	#124×C₇₉	C₂³	1	16	yes	complemented
207	#121×C₇₉	C₂³	1	16	yes	complemented
208	#121×C₇₉	C₂³	1	16	yes	complemented
209	#120×C₇₉	C₂³	1	16	yes	complemented
210	#120×C₇₉	C₂³	1	16	yes	complemented
211	#117×C₇₉	C₂³	1	8	yes	complemented
212	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
215	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
216	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
217	C₂³×D₇₉	—	4	8	no	—
218	C₂³×D₇₉	—	4	8	no	—
219	C₂³×D₇₉	—	4	8	no	—
220	C₂³×D₇₉	—	4	8	no	—
221	C₂³×D₇₉	—	4	4	no	—
222	C₂³×D₇₉	C₂⁴	1	4	yes	—
223	C₂³×D₇₉	C₂⁴	1	2	yes	—
224	C₂³×D₇₉	C₂⁴	1	8	yes	—
225	C₂³×D₇₉	C₂⁴	1	16	yes	—
226	#11929624	—	4	16	no	—
227	#11929623	—	4	64	no	—
228	C₂×Dic₁₅₈	—	4	8	no	—
229	C₂×Dic₁₅₈	—	4	2	no	—
230	C₂×Dic₁₅₈	C₂⁴	1	16	yes	—
231	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
232	C₂×D₃₁₆	—	2	8	no	—
233	C₂×D₃₁₆	—	4	2	no	—
234	C₂×D₃₁₆	—	4	8	no	—
235	C₂×D₃₁₆	—	4	4	no	—
236	C₂×D₃₁₆	—	4	16	no	—
237	C₂×D₃₁₆	C₂⁴	1	8	yes	—
238	C₂×D₃₁₆	C₂⁴	1	4	yes	—
239	C₂×D₃₁₆	C₂⁴	1	8	yes	—
240	C₂×D₃₁₆	C₂⁴	1	16	yes	—
241	C₂×C₂²⋊D₇₉	—	2	8	no	—
242	C₂×C₂²⋊D₇₉	—	2	16	no	—
243	C₂×C₂²⋊D₇₉	—	2	8	no	—
244	C₂×C₂²⋊D₇₉	—	4	64	no	—
245	C₂×C₂²⋊D₇₉	—	4	8	no	—
246	C₂×C₂²⋊D₇₉	—	4	8	no	—
247	C₂×C₂²⋊D₇₉	—	4	4	no	—
248	C₂×C₂²⋊D₇₉	—	4	8	no	—
249	C₂×C₂²⋊D₇₉	—	4	8	no	—
250	C₂×C₂²⋊D₇₉	—	4	8	no	—
251	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
252	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
253	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
254	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
255	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
256	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
257	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
258	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
259	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
260	D₄×D₇₉	—	4	64	no	—
261	D₄×D₇₉	—	4	32	no	—
262	C₂²×Dic₇₉	—	2	8	no	—
263	C₂²×Dic₇₉	—	2	16	no	—
264	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
265	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
266	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
267	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
268	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
269	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
270	C₂×C₄×D₇₉	—	2	16	no	—
271	C₂×C₄×D₇₉	—	2	8	no	—
272	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
273	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
274	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
275	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
276	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
277	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
278	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
279	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
280	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
281	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
282	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
283	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
284	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
285	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
286	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
287	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
288	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
289	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
290	C₄×Dic₇₉	C₂⁴	1	4	yes	—
291	C₄×Dic₇₉	C₂⁴	1	8	yes	—
292	C₄×Dic₇₉	C₂⁴	1	4	yes	—
293	C₄×Dic₇₉	C₂⁴	1	8	yes	—
294	C₄×Dic₇₉	C₂⁴	1	16	yes	—
295	C₂⁴×C₇₉	—	4	4	no	—
296	C₂⁴×C₇₉	—	4	8	no	—
297	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
298	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
299	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
300	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
301	C₂⁴×C₇₉	C₂⁴	1	8	yes	—
302	#41×C₇₉	—	4	16	no	—
303	C₂×Q₈×C₇₉	—	4	2	no	—
304	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
305	C₂×D₄×C₇₉	—	2	8	no	—
306	C₂×D₄×C₇₉	—	4	16	no	—
307	C₂×D₄×C₇₉	—	4	8	no	—
308	C₂×D₄×C₇₉	—	4	4	no	—
309	C₂×D₄×C₇₉	—	4	2	no	—
310	C₂×D₄×C₇₉	—	4	2	no	—
311	C₂×D₄×C₇₉	—	4	2	no	—
312	C₂×D₄×C₇₉	—	4	8	no	—
313	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
314	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
315	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
316	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
317	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
318	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
319	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
320	C₂²×C₄×C₇₉	—	2	4	no	—
321	C₂²×C₄×C₇₉	—	2	4	no	—
322	C₂²×C₄×C₇₉	—	2	4	no	—
323	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
324	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
326	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
329	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
330	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
331	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
332	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
333	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
334	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
335	C₄²×C₇₉	C₂⁴	1	8	yes	—
336	C₂³×C₇₉	—	2	4	no	—
337	C₂³×C₇₉	—	2	8	no	—
338	C₂³×C₇₉	—	2	4	no	—
339	C₂³×C₇₉	—	2	8	no	—
340	C₂³×C₇₉	—	2	4	no	—
341	C₂³×C₇₉	—	2	2	no	—
342	C₂³×C₇₉	—	2	8	no	—
343	C₂³×C₇₉	—	2	2	no	—
344	C₂³×C₇₉	—	2	2	no	—
345	C₂³×C₇₉	—	4	16	no	—
346	C₂³×C₇₉	—	4	8	no	—
347	C₂³×C₇₉	—	8	16	no	—
348	C₂³×C₇₉	C₂⁵	1	2	yes	—
349	C₂³×C₇₉	C₂⁵	1	8	yes	—
350	C₂³×C₇₉	C₂⁵	1	2	yes	—
351	C₂³×C₇₉	C₂⁵	1	2	yes	—
352	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
353	C₂²×D₇₉	—	2	8	no	—
354	C₂²×D₇₉	—	2	4	no	—
355	C₂²×D₇₉	—	2	4	no	—
356	C₂²×D₇₉	—	2	8	no	—
357	C₂²×D₇₉	—	2	4	no	—
358	C₂²×D₇₉	—	2	8	no	—
359	C₂²×D₇₉	—	4	16	no	—
360	C₂²×D₇₉	—	4	16	no	—
361	C₂²×D₇₉	—	4	16	no	—
362	C₂²×D₇₉	—	4	16	no	—
363	C₂²×D₇₉	—	4	8	no	—
364	C₂²×D₇₉	—	8	16	no	—
365	C₂²×D₇₉	—	8	32	no	—
366	C₂²×D₇₉	C₂⁵	1	4	yes	—
367	C₂²×D₇₉	C₂⁵	1	8	yes	—
368	Q₈×C₇₉	—	4	4	no	—
369	D₄×C₇₉	—	2	16	no	—
370	D₄×C₇₉	—	4	16	no	—
371	D₄×C₇₉	—	4	16	no	—
372	D₄×C₇₉	—	4	8	no	—
373	D₄×C₇₉	—	4	4	no	—
374	D₄×C₇₉	—	4	4	no	—
375	D₄×C₇₉	—	4	4	no	—
376	C₂×C₄×C₇₉	—	2	8	no	—
377	C₂×C₄×C₇₉	—	2	2	no	—
378	C₂×C₄×C₇₉	—	2	2	no	—
379	C₂×C₄×C₇₉	—	2	2	no	—
380	C₂×C₄×C₇₉	—	2	8	no	—
381	C₂×C₄×C₇₉	—	2	8	no	—
382	C₂×C₄×C₇₉	—	2	8	no	—
383	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
384	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
385	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
386	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
387	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
388	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
389	C₂²⋊D₇₉	—	2	16	no	—
390	C₂²⋊D₇₉	—	2	32	no	—
391	C₂²⋊D₇₉	—	2	16	no	—
392	C₂²⋊D₇₉	—	4	16	no	—
393	C₂²⋊D₇₉	—	4	16	no	—
394	C₂²⋊D₇₉	—	4	16	no	—
395	C₂²⋊D₇₉	—	4	16	no	—
396	C₂²⋊D₇₉	—	4	16	no	—
397	C₂²⋊D₇₉	—	4	8	no	—
398	C₂×Dic₇₉	—	2	4	no	—
399	C₂×Dic₇₉	—	2	8	no	—
400	C₂×Dic₇₉	—	2	4	no	—
401	C₂×Dic₇₉	—	2	32	no	—
402	C₂×Dic₇₉	—	2	16	no	—
403	C₂×Dic₇₉	H(5,𝔽₂)	1	8	yes	—
404	C₂×Dic₇₉	C₂⁵	1	4	yes	—
405	C₂×Dic₇₉	C₂⁵	1	8	yes	—
406	C₂×Dic₇₉	C₂⁵	1	4	yes	—
407	C₂×Dic₇₉	C₂⁵	1	4	yes	—
408	D₃₁₆	—	2	16	no	—
409	D₃₁₆	—	4	16	no	—
410	D₃₁₆	—	4	8	no	—
411	D₃₁₆	—	4	4	no	—
412	C₄×D₇₉	—	2	16	no	—
413	C₄×D₇₉	—	2	32	no	—
414	Dic₁₅₈	—	4	16	no	—
415	Dic₁₅₈	—	4	4	no	—
416	C₂²×C₇₉	—	2	4	no	—
417	C₂²×C₇₉	—	2	8	no	—
418	C₂²×C₇₉	—	2	4	no	—
419	C₂²×C₇₉	—	2	2	no	—
420	C₂²×C₇₉	—	2	4	no	—
421	C₂²×C₇₉	—	2	8	no	—
422	C₂²×C₇₉	—	2	8	no	—
423	C₂²×C₇₉	—	2	2	no	—
424	C₂²×C₇₉	—	2	2	no	—
425	C₂²×C₇₉	—	4	4	no	—
426	C₂²×C₇₉	—	4	16	no	—
427	C₂²×C₇₉	—	4	4	no	—
428	C₂²×C₇₉	—	4	4	no	—
429	C₂²×C₇₉	—	8	16	no	—
430	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
431	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
432	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
433	C₂×D₇₉	—	2	4	no	—
434	C₂×D₇₉	—	2	8	no	—
435	C₂×D₇₉	—	2	4	no	—
436	C₂×D₇₉	—	2	8	no	—
437	C₂×D₇₉	—	2	4	no	—
438	C₂×D₇₉	—	2	8	no	—
439	C₂×D₇₉	—	4	16	no	—
440	C₂×D₇₉	—	4	8	no	—
441	C₂×D₇₉	—	8	16	no	—
442	C₂×D₇₉	—	8	32	no	—
443	C₄×C₇₉	—	2	2	no	—
444	C₄×C₇₉	—	2	2	no	—
445	C₄×C₇₉	—	2	2	no	—
446	C₄×C₇₉	—	2	8	no	—
447	C₄×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
448	Dic₇₉	—	2	4	no	—
449	Dic₇₉	—	2	8	no	—
450	Dic₇₉	—	2	4	no	—
451	Dic₇₉	C₂×H(5,𝔽₂)	1	8	yes	—
452	C₂×#3549	—	79	1	no	maximal, Sylow
453	C₂×C₇₉	—	4	2	no	—
454	C₂×C₇₉	—	4	8	no	—
455	C₂×C₇₉	—	4	2	no	—
456	C₂×C₇₉	—	4	2	no	—
457	C₂×C₇₉	#3549	1	4	yes	complemented
458	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	2	yes	—
459	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
460	D₇₉	—	4	4	no	—
461	D₇₉	—	4	8	no	—
462	#3549	—	79	32	no	—
463	C₂×H(3,𝔽₄)	—	79	2	no	—
464	C₂×H(3,𝔽₄)	—	79	2	no	—
465	C₂×#555	—	79	2	no	—
466	C₂×#555	—	79	2	no	—
467	C₂×#555	—	79	2	no	—
468	C₂×D₄²	—	79	2	no	—
469	C₂×D₄²	—	79	2	no	—
470	C₂×D₄²	—	79	2	no	—
471	C₂×#535	—	79	1	no	—
472	C₂×#535	—	79	4	no	—
473	C₂×#535	—	79	2	no	—
474	C₂×#535	—	79	4	no	—
475	C₂×#535	D₇₉	1	1	yes	characteristic, complemented
476	C₂×#532	—	79	1	no	—
477	C₂×#532	—	79	2	no	—
478	C₇₉	C₂×#3549	1	1	yes	characteristic, complemented, Sylow
479	C₂²×#41	—	79	4	no	—
480	C₂²×#41	—	79	1	no	—
481	C₂²×#41	C₂×D₇₉	1	1	yes	characteristic, complemented
482	C₂³×D₄	—	79	4	no	—
483	C₂³×D₄	—	79	2	no	—
484	C₂³×D₄	—	79	4	no	—
485	C₂³×D₄	—	79	1	no	—
486	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
487	H(3,𝔽₄)	—	79	32	no	—
488	H(3,𝔽₄)	—	79	32	no	—
489	#555	—	79	32	no	—
490	#555	—	79	32	no	—
491	#555	—	79	32	no	—
492	D₄²	—	79	32	no	—
493	D₄²	—	79	32	no	—
494	D₄²	—	79	32	no	—
495	#535	—	79	16	no	—
496	#535	—	79	64	no	—
497	#535	—	79	32	no	—
498	#535	—	79	64	no	—
499	#535	C₂×D₇₉	1	16	yes	complemented
500	#532	—	79	16	no	—
501	#532	—	79	32	no	—
502	C₂×C₄⋊Q₈	—	79	1	no	—
503	C₂×C₄⋊Q₈	—	79	2	no	—
504	C₂×#127	—	79	2	no	—
505	C₂×#127	—	79	1	no	—
506	C₂×#127	—	79	4	no	—
507	C₂×#127	—	79	2	no	—
508	C₂×#127	C₂×D₇₉	1	2	yes	complemented
509	C₂×#124	—	79	1	no	—
510	C₂×#124	—	79	2	no	—
511	C₂×#124	—	79	1	no	—
512	C₂×#124	—	79	4	no	—
513	C₂×#124	—	79	4	no	—
514	C₂×#124	—	79	4	no	—
515	C₂×#124	—	79	4	no	—
516	C₂×#124	—	79	4	no	—
517	C₂×#124	—	79	4	no	—
518	C₂×#124	C₂×D₇₉	1	2	yes	complemented
519	C₂×#121	—	79	2	no	—
520	C₂×#121	—	79	4	no	—
521	C₂×#121	—	79	2	no	—
522	C₂×#121	—	79	2	no	—
523	C₂×#121	—	79	4	no	—
524	C₂×#121	—	79	4	no	—
525	C₂×#121	—	79	2	no	—
526	C₂×#121	—	79	2	no	—
527	C₂×#121	—	79	2	no	—
528	C₂×#121	—	79	4	no	—
529	C₂×#121	—	79	4	no	—
530	C₂×#121	C₂×D₇₉	1	2	yes	complemented
531	C₂×#121	C₂×D₇₉	1	2	yes	complemented
532	C₂×#120	—	79	4	no	—
533	C₂×#120	—	79	2	no	—
534	C₂×#120	—	79	4	no	—
535	C₂×#120	—	79	2	no	—
536	C₂×#120	—	79	4	no	—
537	C₂×#120	—	79	4	no	—
538	C₂×#120	—	79	4	no	—
539	C₂×#120	—	79	4	no	—
540	C₂×#120	C₂×D₇₉	1	2	yes	complemented
541	C₂×#120	C₂×D₇₉	1	2	yes	complemented
542	C₂×C₄×D₄	—	79	2	no	—
543	C₂×C₄×D₄	—	79	2	no	—
544	C₂×C₄×D₄	—	79	2	no	—
545	C₂×C₄×D₄	—	79	2	no	—
546	C₂×C₄×D₄	—	79	4	no	—
547	C₂×#117	—	79	1	no	—
548	C₂×#117	—	79	2	no	—
549	C₂×#117	—	79	4	no	—
550	C₂×#117	—	79	4	no	—
551	C₂×#117	C₂×D₇₉	1	1	yes	characteristic, complemented
552	C₂²×C₄²	—	79	1	no	—
553	C₂⁵	—	79	2	no	—
554	C₂⁵	—	79	4	no	—
555	C₂⁵	C₂²×D₇₉	1	2	yes	—
556	C₂×#41	—	4	4	no	—
557	C₂×#41	—	316	4	no	—
558	C₂×#41	—	316	16	no	—
559	C₂×#41	—	79	32	no	—
560	C₂×#41	—	79	8	no	—
561	C₂×#41	C₂²×D₇₉	1	8	yes	complemented
562	C₂²×Q₈	—	79	4	no	—
563	C₂²×Q₈	—	79	1	no	—
564	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
565	C₂²×D₄	—	4	4	no	—
566	C₂²×D₄	—	316	4	no	—
567	C₂²×D₄	—	316	8	no	—
568	C₂²×D₄	—	316	16	no	—
569	C₂²×D₄	—	316	16	no	—
570	C₂²×D₄	—	79	4	no	—
571	C₂²×D₄	—	79	4	no	—
572	C₂²×D₄	—	79	4	no	—
573	C₂²×D₄	—	79	4	no	—
574	C₂²×D₄	—	79	2	no	—
575	C₂²×D₄	—	79	4	no	—
576	C₂²×D₄	—	79	32	no	—
577	C₂²×D₄	—	79	16	no	—
578	C₂²×D₄	—	79	32	no	—
579	C₂²×D₄	—	79	2	no	—
580	C₂²×D₄	—	79	4	no	—
581	C₂²×D₄	—	79	2	no	—
582	C₂²×D₄	—	79	1	no	—
583	C₂²×D₄	—	79	2	no	—
584	C₂²×D₄	—	79	4	no	—
585	C₂²×D₄	—	79	8	no	—
586	C₂²×D₄	—	79	2	no	—
587	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
588	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
589	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
590	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
591	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
592	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
593	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
594	C₂²×D₄	C₂²×D₇₉	1	8	yes	complemented
595	C₂³×C₄	—	79	4	no	—
596	C₂³×C₄	—	79	2	no	—
597	C₂³×C₄	—	79	4	no	—
598	C₂³×C₄	—	79	2	no	—
599	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
600	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
601	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
602	C₄⋊Q₈	—	79	8	no	—
603	C₄⋊Q₈	—	79	16	no	—
604	#127	—	79	16	no	—
605	#127	—	79	8	no	—
606	#127	—	79	32	no	—
607	#127	—	79	16	no	—
608	#127	C₂²×D₇₉	1	16	yes	complemented
609	#124	—	79	8	no	—
610	#124	—	79	16	no	—
611	#124	—	79	8	no	—
612	#124	—	79	32	no	—
613	#124	—	79	32	no	—
614	#124	—	79	32	no	—
615	#124	—	79	32	no	—
616	#124	—	79	32	no	—
617	#124	—	79	32	no	—
618	#124	C₂²×D₇₉	1	16	yes	complemented
619	#121	—	79	16	no	—
620	#121	—	79	32	no	—
621	#121	—	79	16	no	—
622	#121	—	79	16	no	—
623	#121	—	79	32	no	—
624	#121	—	79	32	no	—
625	#121	—	79	16	no	—
626	#121	—	79	16	no	—
627	#121	—	79	16	no	—
628	#121	—	79	32	no	—
629	#121	—	79	32	no	—
630	#121	C₂²×D₇₉	1	16	yes	complemented
631	#121	C₂²×D₇₉	1	16	yes	complemented
632	#120	—	79	32	no	—
633	#120	—	79	16	no	—
634	#120	—	79	32	no	—
635	#120	—	79	16	no	—
636	#120	—	79	32	no	—
637	#120	—	79	32	no	—
638	#120	—	79	32	no	—
639	#120	—	79	32	no	—
640	#120	C₂²×D₇₉	1	16	yes	complemented
641	#120	C₂²×D₇₉	1	16	yes	complemented
642	C₄×D₄	—	79	16	no	—
643	C₄×D₄	—	79	16	no	—
644	C₄×D₄	—	79	16	no	—
645	C₄×D₄	—	79	16	no	—
646	C₄×D₄	—	79	32	no	—
647	#117	—	79	8	no	—
648	#117	—	79	16	no	—
649	#117	—	79	32	no	—
650	#117	—	79	32	no	—
651	#117	C₂²×D₇₉	1	8	yes	complemented
652	C₂×C₄⋊C₄	—	79	2	no	—
653	C₂×C₄⋊C₄	—	79	4	no	—
654	C₂×C₄⋊C₄	—	79	2	no	—
655	C₂×C₄⋊C₄	—	79	2	no	—
656	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
657	C₂×C₂²⋊C₄	—	79	2	no	—
658	C₂×C₂²⋊C₄	—	79	4	no	—
659	C₂×C₂²⋊C₄	—	79	2	no	—
660	C₂×C₂²⋊C₄	—	79	4	no	—
661	C₂×C₂²⋊C₄	—	79	2	no	—
662	C₂×C₂²⋊C₄	—	79	4	no	—
663	C₂×C₂²⋊C₄	—	79	4	no	—
664	C₂×C₂²⋊C₄	—	79	4	no	—
665	C₂×C₂²⋊C₄	—	79	2	no	—
666	C₂×C₂²⋊C₄	—	79	4	no	—
667	C₂×C₂²⋊C₄	—	79	2	no	—
668	C₂×C₂²⋊C₄	—	79	4	no	—
669	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
670	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
672	C₂×C₄²	—	79	2	no	—
673	C₂×C₄²	—	79	4	no	—
674	C₂×C₄²	—	79	1	no	—
675	C₂×C₄²	—	79	2	no	—
676	C₂×C₄²	—	79	1	no	—
677	C₂×C₄²	—	79	8	no	—
678	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
679	C₂⁴	—	4	4	no	—
680	C₂⁴	—	4	8	no	—
681	C₂⁴	—	316	8	no	—
682	C₂⁴	—	316	8	no	—
683	C₂⁴	—	316	8	no	—
684	C₂⁴	—	316	4	no	—
685	C₂⁴	—	316	8	no	—
686	C₂⁴	—	79	8	no	—
687	C₂⁴	—	79	16	no	—
688	C₂⁴	—	79	4	no	—
689	C₂⁴	—	79	2	no	—
690	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
691	C₂⁴	C₂³×D₇₉	1	4	yes	—
692	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
693	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
694	C₂⁴	C₂³×D₇₉	1	8	yes	—
695	#41	—	4	16	no	—
696	#41	—	316	16	no	—
697	#41	—	316	64	no	—
698	C₂×Q₈	—	4	2	no	—
699	C₂×Q₈	—	316	8	no	—
700	C₂×Q₈	—	316	2	no	—
701	C₂×Q₈	—	79	16	no	—
702	C₂×Q₈	—	79	4	no	—
703	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
704	C₂×D₄	—	2	8	no	—
705	C₂×D₄	—	4	16	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	—	4	8	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	8	no	—
712	C₂×D₄	—	316	8	no	—
713	C₂×D₄	—	316	4	no	—
714	C₂×D₄	—	316	2	no	—
715	C₂×D₄	—	316	16	no	—
716	C₂×D₄	—	316	32	no	—
717	C₂×D₄	—	316	64	no	—
718	C₂×D₄	—	316	8	no	—
719	C₂×D₄	—	316	8	no	—
720	C₂×D₄	—	316	8	no	—
721	C₂×D₄	—	316	8	no	—
722	C₂×D₄	—	316	8	no	—
723	C₂×D₄	—	316	4	no	—
724	C₂×D₄	—	316	64	no	—
725	C₂×D₄	—	79	16	no	—
726	C₂×D₄	—	79	16	no	—
727	C₂×D₄	—	79	16	no	—
728	C₂×D₄	—	79	16	no	—
729	C₂×D₄	—	79	16	no	—
730	C₂×D₄	—	79	8	no	—
731	C₂×D₄	—	79	8	no	—
732	C₂×D₄	—	79	16	no	—
733	C₂×D₄	—	79	8	no	—
734	C₂×D₄	—	79	4	no	—
735	C₂×D₄	—	79	8	no	—
736	C₂×D₄	—	79	16	no	—
737	C₂×D₄	—	79	8	no	—
738	C₂×D₄	—	158	8	no	—
739	C₂×D₄	—	158	16	no	—
740	C₂×D₄	—	158	8	no	—
741	C₂×D₄	—	158	8	no	—
742	C₂×D₄	C₂³×D₇₉	1	8	yes	—
743	C₂×D₄	C₂³×D₇₉	1	4	yes	—
744	C₂×D₄	C₂³×D₇₉	1	8	yes	—
745	C₂×D₄	C₂³×D₇₉	1	4	yes	—
746	C₂×D₄	C₂³×D₇₉	1	16	yes	—
747	C₂×D₄	C₂³×D₇₉	1	16	yes	—
748	C₂×D₄	C₂³×D₇₉	1	4	yes	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	79	2	no	—
753	C₂²×C₄	—	79	8	no	—
754	C₂²×C₄	—	79	16	no	—
755	C₂²×C₄	—	79	2	no	—
756	C₂²×C₄	—	79	4	no	—
757	C₂²×C₄	—	79	2	no	—
758	C₂²×C₄	—	79	16	no	—
759	C₂²×C₄	—	79	8	no	—
760	C₂²×C₄	—	158	16	no	—
761	C₂²×C₄	—	158	16	no	—
762	C₂²×C₄	—	158	8	no	—
763	C₂²×C₄	—	158	8	no	—
764	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
765	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
766	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
767	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
768	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
769	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
770	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
771	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
772	C₄⋊C₄	—	79	8	no	—
773	C₄⋊C₄	—	79	16	no	—
774	C₄⋊C₄	—	79	8	no	—
775	C₄⋊C₄	—	79	8	no	—
776	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
777	C₂²⋊C₄	—	79	8	no	—
778	C₂²⋊C₄	—	79	16	no	—
779	C₂²⋊C₄	—	79	8	no	—
780	C₂²⋊C₄	—	79	16	no	—
781	C₂²⋊C₄	—	79	8	no	—
782	C₂²⋊C₄	—	79	16	no	—
783	C₂²⋊C₄	—	79	16	no	—
784	C₂²⋊C₄	—	79	16	no	—
785	C₂²⋊C₄	—	79	8	no	—
786	C₂²⋊C₄	—	79	16	no	—
787	C₂²⋊C₄	—	79	8	no	—
788	C₂²⋊C₄	—	79	16	no	—
789	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
790	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
791	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
792	C₄²	—	79	4	no	—
793	C₄²	—	79	8	no	—
794	C₄²	—	79	4	no	—
795	C₄²	—	79	8	no	—
796	C₄²	—	79	16	no	—
797	C₄²	C₂³×D₇₉	1	8	yes	—
798	C₂³	—	2	4	no	—
799	C₂³	—	2	8	no	—
800	C₂³	—	2	4	no	—
801	C₂³	—	2	8	no	—
802	C₂³	—	2	4	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	8	no	—
807	C₂³	—	4	8	no	—
808	C₂³	—	4	16	no	—
809	C₂³	—	8	16	no	—
810	C₂³	—	316	16	no	—
811	C₂³	—	316	16	no	—
812	C₂³	—	316	16	no	—
813	C₂³	—	316	8	no	—
814	C₂³	—	316	16	no	—
815	C₂³	—	79	8	no	—
816	C₂³	—	79	4	no	—
817	C₂³	—	632	32	no	—
818	C₂³	—	632	16	no	—
819	C₂³	—	158	8	no	—
820	C₂³	—	158	4	no	—
821	C₂³	—	158	8	no	—
822	C₂³	—	158	4	no	—
823	C₂³	—	158	4	no	—
824	C₂³	—	158	8	no	—
825	C₂³	C₂⁴×D₇₉	1	2	yes	—
826	C₂³	C₂⁴×D₇₉	1	8	yes	—
827	C₂³	C₂⁴×D₇₉	1	2	yes	—
828	C₂³	C₂⁴×D₇₉	1	2	yes	—
829	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
830	Q₈	—	4	4	no	—
831	Q₈	—	316	16	no	—
832	Q₈	—	316	4	no	—
833	D₄	—	2	16	no	—
834	D₄	—	4	8	no	—
835	D₄	—	4	16	no	—
836	D₄	—	4	4	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	4	no	—
839	D₄	—	4	16	no	—
840	D₄	—	316	16	no	—
841	D₄	—	316	8	no	—
842	D₄	—	316	4	no	—
843	D₄	—	316	16	no	—
844	D₄	—	316	16	no	—
845	D₄	—	316	16	no	—
846	D₄	—	316	16	no	—
847	D₄	—	316	16	no	—
848	D₄	—	316	8	no	—
849	D₄	—	158	16	no	—
850	D₄	—	158	32	no	—
851	D₄	—	158	16	no	—
852	D₄	—	158	16	no	—
853	C₂×C₄	—	2	8	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	8	no	—
858	C₂×C₄	—	2	8	no	—
859	C₂×C₄	—	2	8	no	—
860	C₂×C₄	—	79	8	no	—
861	C₂×C₄	—	79	4	no	—
862	C₂×C₄	—	79	4	no	—
863	C₂×C₄	—	79	8	no	—
864	C₂×C₄	—	79	4	no	—
865	C₂×C₄	—	158	32	no	—
866	C₂×C₄	—	158	32	no	—
867	C₂×C₄	—	158	16	no	—
868	C₂×C₄	—	158	8	no	—
869	C₂×C₄	—	158	4	no	—
870	C₂×C₄	—	158	4	no	—
871	C₂×C₄	—	158	16	no	—
872	C₂×C₄	#14579206	1	4	yes	—
873	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
874	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
875	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
876	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
877	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
878	C₂²	—	2	4	no	—
879	C₂²	—	2	8	no	—
880	C₂²	—	2	4	no	—
881	C₂²	—	2	8	no	—
882	C₂²	—	2	4	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	8	no	—
887	C₂²	—	4	4	no	—
888	C₂²	—	4	16	no	—
889	C₂²	—	4	4	no	—
890	C₂²	—	4	4	no	—
891	C₂²	—	8	16	no	—
892	C₂²	—	316	16	no	—
893	C₂²	—	316	8	no	—
894	C₂²	—	632	32	no	—
895	C₂²	—	632	16	no	—
896	C₂²	—	158	8	no	—
897	C₂²	—	158	4	no	—
898	C₂²	—	158	8	no	—
899	C₂²	—	158	4	no	—
900	C₂²	—	158	4	no	—
901	C₂²	—	158	8	no	—
902	C₂²	H(5,𝔽₂)×D₇₉	1	4	yes	—
903	C₂²	C₂×#14579206	1	2	yes	—
904	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
905	C₄	—	2	8	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	2	no	—
908	C₄	—	2	2	no	—
909	C₄	—	79	8	no	—
910	C₄	—	158	8	no	—
911	C₄	—	158	4	no	—
912	C₄	—	158	4	no	—
913	C₄	C₂×#14579206	1	4	yes	—
914	C₂	—	4	2	no	—
915	C₂	—	4	8	no	—
916	C₂	—	4	2	no	—
917	C₂	—	4	2	no	—
918	C₂	—	316	8	no	—
919	C₂	—	316	4	no	—
920	C₂	#23777803	1	4	yes	direct product factor
921	C₂	C₂×H(5,𝔽₂)×D₇₉	1	2	yes	—
922	C₂	C₂²×#14579206	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#535×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#535	D₇₉
hypocenter	C₇₉	C₂×#3549
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#535

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #23777803	C₂	direct (N × H)
2. C₂×#19099306	C₂	semidirect
3. C₂×#19099305	C₂	semidirect
4. C₂×#19099277	C₂	semidirect
5. C₂×#19099276	C₂	semidirect
6. C₂×#19099275	C₂	semidirect
7. C₂×#19099197	C₂	semidirect
8. C₂×D₄×C₂²⋊D₇₉	C₂	semidirect
9. C₂×#19099195	C₂	semidirect
10. C₂×#19099129	C₂	semidirect
11. C₂×#19099128	C₂	semidirect
12. C₂×#19099127	C₂	semidirect
13. C₂×#19099126	C₂	semidirect
14. C₂×#19099109	C₂	semidirect
15. C₂×#19099108	C₂	semidirect
16. C₂×#535×C₇₉	C₂	semidirect
17. C₂²×#11929624	C₂²	semidirect
18. C₂²×#11929623	C₂²	semidirect
19. C₂³×D₃₁₆	C₂²	semidirect
20. C₂³×C₂²⋊D₇₉	C₂²	semidirect
21. C₂²×D₄×D₇₉	C₂²	semidirect
22. C₂²×D₄×D₇₉	C₂²	semidirect
23. #19099306	C₂²	semidirect
24. #19099305	C₂²	semidirect
25. #19099277	C₂²	semidirect
26. #19099276	C₂²	semidirect
27. #19099275	C₂²	semidirect
28. #19099197	C₂²	semidirect
29. D₄×C₂²⋊D₇₉	C₂²	semidirect
30. #19099195	C₂²	semidirect
31. #19099129	C₂²	semidirect
32. #19099128	C₂²	semidirect
33. #19099127	C₂²	semidirect
34. #19099126	C₂²	semidirect
35. #19099109	C₂²	semidirect
36. #19099108	C₂²	semidirect
37. C₂×#14579160	C₂²	semidirect
38. C₂×#14579159	C₂²	semidirect
41. C₂×#14579157	C₂²	semidirect
42. C₂×#14579157	C₂²	semidirect
43. C₂×#14579150	C₂²	semidirect
44. C₂×#14579150	C₂²	semidirect
45. C₂×#14579149	C₂²	semidirect
46. C₂×#14579148	C₂²	semidirect
47. C₂×#14579148	C₂²	semidirect
48. C₂×#14579147	C₂²	semidirect
49. C₂×#14579147	C₂²	semidirect
50. C₂×#14579147	C₂²	semidirect
51. C₂×#14579147	C₂²	semidirect
52. C₂×#14579136	C₂²	semidirect
53. C₂×#14579135	C₂²	semidirect
54. C₂×#14579135	C₂²	semidirect
55. C₂×#14579134	C₂²	semidirect
56. C₂×#14579134	C₂²	semidirect
57. C₂×#14579133	C₂²	semidirect
58. C₂×#14579133	C₂²	semidirect
59. C₂×#14579133	C₂²	semidirect
60. C₂×#14579133	C₂²	semidirect
61. C₂×#14579133	C₂²	semidirect
62. C₂×#14579132	C₂²	semidirect
63. C₂×#14579131	C₂²	semidirect
64. C₂×#14579131	C₂²	semidirect
65. C₂×#14579130	C₂²	semidirect
66. C₂×#14579129	C₂²	semidirect
67. C₂×#14579129	C₂²	semidirect
68. C₂×#14579129	C₂²	semidirect
69. C₂×#14579129	C₂²	semidirect
70. C₂×#14579129	C₂²	semidirect
71. C₂×D₄×Dic₇₉	C₂²	semidirect
72. C₂×#14579123	C₂²	semidirect
73. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
74. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
75. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
76. C₂×#14579120	C₂²	semidirect
77. C₂×#14579119	C₂²	semidirect
78. C₂×#14579118	C₂²	semidirect
79. C₂×#14579117	C₂²	semidirect
80. C₂²×C₄×Dic₇₉	C₂²	semidirect
81. C₂²×#41×C₇₉	C₂²	semidirect
82. C₂³×D₄×C₇₉	C₂²	semidirect
83. #535×C₇₉	C₂²	semidirect
84. C₂×#127×C₇₉	C₂²	semidirect
85. C₂×#124×C₇₉	C₂²	semidirect
86. C₂×#121×C₇₉	C₂²	semidirect
87. C₂×#121×C₇₉	C₂²	semidirect
88. C₂×#120×C₇₉	C₂²	semidirect
89. C₂×#120×C₇₉	C₂²	semidirect
90. C₂×#117×C₇₉	C₂²	semidirect
94. C₂×#11929624	C₂³	semidirect
96. C₂×#11929623	C₂³	semidirect
104. C₂²×D₃₁₆	C₂³	semidirect
115. C₂²×C₂²⋊D₇₉	C₂³	semidirect
118. C₂×D₄×D₇₉	C₂³	semidirect
119. C₂×D₄×D₇₉	C₂³	semidirect
124. #14579160	C₂³	semidirect
125. #14579159	C₂³	semidirect
128. #14579157	C₂³	semidirect
129. #14579157	C₂³	semidirect
130. #14579150	C₂³	semidirect
131. #14579150	C₂³	semidirect
132. #14579149	C₂³	semidirect
133. #14579148	C₂³	semidirect
134. #14579148	C₂³	semidirect
135. #14579147	C₂³	semidirect
136. #14579147	C₂³	semidirect
137. #14579147	C₂³	semidirect
138. #14579147	C₂³	semidirect
139. #14579136	C₂³	semidirect
140. #14579135	C₂³	semidirect
141. #14579135	C₂³	semidirect
142. #14579134	C₂³	semidirect
143. #14579134	C₂³	semidirect
144. #14579133	C₂³	semidirect
145. #14579133	C₂³	semidirect
146. #14579133	C₂³	semidirect
147. #14579133	C₂³	semidirect
148. #14579133	C₂³	semidirect
149. #14579132	C₂³	semidirect
150. #14579131	C₂³	semidirect
151. #14579131	C₂³	semidirect
152. #14579130	C₂³	semidirect
153. #14579129	C₂³	semidirect
154. #14579129	C₂³	semidirect
155. #14579129	C₂³	semidirect
156. #14579129	C₂³	semidirect
157. #14579129	C₂³	semidirect
158. D₄×Dic₇₉	C₂³	semidirect
159. #14579123	C₂³	semidirect
160. C₄×C₂²⋊D₇₉	C₂³	semidirect
161. C₄×C₂²⋊D₇₉	C₂³	semidirect
162. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
163. #14579120	C₂³	semidirect
164. #14579119	C₂³	semidirect
165. #14579118	C₂³	semidirect
166. #14579117	C₂³	semidirect
188. C₂×C₄×Dic₇₉	C₂³	semidirect
191. C₂×#41×C₇₉	C₂³	semidirect
201. C₂²×D₄×C₇₉	C₂³	semidirect
205. #127×C₇₉	C₂³	semidirect
206. #124×C₇₉	C₂³	semidirect
207. #121×C₇₉	C₂³	semidirect
208. #121×C₇₉	C₂³	semidirect
209. #120×C₇₉	C₂³	semidirect
210. #120×C₇₉	C₂³	semidirect
211. #117×C₇₉	C₂³	semidirect
457. C₂×C₇₉	#3549	semidirect
475. C₂×#535	D₇₉	semidirect
478. C₇₉	C₂×#3549	semidirect
481. C₂²×#41	C₂×D₇₉	semidirect
486. C₂³×D₄	C₂×D₇₉	semidirect
499. #535	C₂×D₇₉	semidirect
508. C₂×#127	C₂×D₇₉	semidirect
518. C₂×#124	C₂×D₇₉	semidirect
530. C₂×#121	C₂×D₇₉	semidirect
531. C₂×#121	C₂×D₇₉	semidirect
540. C₂×#120	C₂×D₇₉	semidirect
541. C₂×#120	C₂×D₇₉	semidirect
551. C₂×#117	C₂×D₇₉	semidirect
561. C₂×#41	C₂²×D₇₉	semidirect
594. C₂²×D₄	C₂²×D₇₉	semidirect
608. #127	C₂²×D₇₉	semidirect
618. #124	C₂²×D₇₉	semidirect
630. #121	C₂²×D₇₉	semidirect
631. #121	C₂²×D₇₉	semidirect
640. #120	C₂²×D₇₉	semidirect
641. #120	C₂²×D₇₉	semidirect
651. #117	C₂²×D₇₉	semidirect
920. C₂	#23777803	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#23777803	2
C₂×#19099306	2
C₂×#19099305	2
C₂×#19099277	2
C₂×#19099276	2
C₂×#19099275	2
C₂×#19099197	2
C₂×D₄×C₂²⋊D₇₉	2
C₂×#19099195	2
C₂×#19099129	2
C₂×#19099128	2
C₂×#19099127	2
C₂×#19099126	2
C₂×#19099109	2
C₂×#19099108	2
C₂×#535×C₇₉	2
C₂×#3549	79

Subgroups — C2×#23777803 #35196068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777803 #35196068